Batch Process
In order to properly compare batch to continuous TFF performance, the batch TFF must be better understood. The process begins with the liposome formation mixture entering the central vessel at the same time as the buffer. At the completion of the liposome formation step, the central vessel contains approximately 30% ethanol, which is slightly less than the undiluted liposome formation mixture due to the dilution from the added buffer stream.
The batch TFF operates as constant volume diafiltration (CVDF) with constant inlet pressure to the hollow fiber. Permeate flow is fully open with no applied back pressure. The buffer stream flow matches the permeate flow to maintain constant volume.
Evaluation of the batch TFF performance showed an unexpected phenomenon. Regardless of the constant inlet pressure, the permeate flow showed an increasing pattern as the diavolumes progressed as opposed to a constant flow. Shown in Figure 2A, permeate flow increased and leveled off through the run. Further assessment of the permeate, showed that the ethanol concentration decreased linearly as the permeate flow increased (Figure 2A), indicating permeate flow and ethanol concentration may be interrelated.
Ethanol (EtOH) would be expected to be removed during TFF in a manner following the standard diafiltration equation (Equation 1) such that\(c_{0}\)= initial EtOH concentration, \(c\)= final EtOH concentration, α = EtOH rejection coefficient and \(\frac{V_{b}}{V_{s}}\) = diavolumes.
\(c=c_{0}e^{-(1-\sigma)\frac{V_{b}}{V_{s}}}\) (Equation 1)
It is common to assume the species being removed is free flowing and has a rejection coefficient of 0. The results in Figure 2A indicate a relationship between the ethanol concentration and the permeate flow. The ethanol most likely has an impact on hollow fiber permeability, which could be expressed as ethanol having a partial rejection coefficient (α). This is not unprecedented as ethanol has shown hollow fiber swelling and impact on permeability in other industrial applications (Otitoju T.A. et al. 2017, Kochan J. et al. 2009).
To assess the ethanol rejection coefficient, the batch process was assessed with the Equation 1 model. Using an inline density measurement on the permeate, the EtOH concentration was calculated across the diavolumes. Applying mass balance for the system, the retentate EtOH concentration was calculated, and the curve fitted to Equation 1 to determine the EtOH rejection coefficient. As shown in Figure 2B, the rejection coefficient (α) calculated to approx. 0.5 as opposed to the zero coefficient that would have been assumed. Additionally, the fit showed the rejection coefficient to be slightly greater than 0.5 early in the process and slightly less than 0.5 later in the process, indicating an ethanol concentration dependency to the rejection coefficient.
While not having a significant impact on the overall batch process, an ethanol concentration dependent rejection coefficient is interesting to consider in a continuous TTF/ILDF system. In the system shown in Figure 1C, the initial hollow fiber pass/stage of the ILDF system would contain higher concentrations of ethanol and would presumably be less efficient/permeable than the later hollow fiber passes/stages. Thus, more passes would be needed to remove the first portion of the ethanol as compared to later portions. Based on this, additional upfront dilution of the initial liposome formation mixture should increase permeability and efficiency and reduce the amount of passes/stages needed in a continuous design.
The ethanol concentration dependency phenomenon was further explored regarding its impact on the continuous ILDF arrangement under the guise that dilution/increased permeability decreases the number of passes/stages needed and increases overall efficiency/benefit of the system.